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Dynamic Problems of Thermoelasticity in Strains for Plane Isotropic Bodies
Джумаёзов, У.З.
Annotaciya
Using the Duhamel-Neumann relationship and the equations of motion, the Saint-Venant compatibility conditions, are written as a system of six dynamic equations with respect to strains. It is shown that, unlike the Beltrami-Michell equations, these equations are independent and can be considered as dynamic equations of thermoelasticity.Considering these equations together with the heat influx equations, a coupled thermoelasticity problem in strains is formulated. It is shown, also that replacing, the first three equations in formulated coupled problem, with the motion equations allows us to set an alternative coupled problem in strains. Using the two proposed formulations the coupled thermoelastic problem on a rectangular plate is numerically solved. The validity of the formulated two boundary value problems of thermoelasticity is justified by comparing their numerical, obtained by the variable direction method and recurrence relations, as well as solving a similar related problem regarding displacements.
термоупругостьусловие совместности Сен-Венанадеформацияконечно-разностный методявная и неявная схемыметод прогонкикраевая задачаthermoelasticitySaint-Venant compatibility conditionstrain
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